Special isoparametric orbits in Riemannian symmetric spaces
type: Item
instance of: scholarly article
title: Special isoparametric orbits in Riemannian symmetric spaces
zbMATH Open document ID: 0832.53042
DOI: 10.1007/BF01266321
author: László Verhóczki
published in: Geometriae Dedicata
publication date: 1996-03-12T00:00:00Z
review text: The author treats principal orbits \(M\) of isotropy subgroups in Riemannian symmetric spaces of compact and non-compact type and shows that these \(M\) are isoparametric submanifolds. Further, he shows that, except in some special cases, the eigenspace distributions of the shape operator with respect to the radial unit vector field are involutive and their integral submanifolds are totally geodesic in \(M\). Finally, it is also shown that these isoparametric submanifolds are curvature-adapted submanifolds.
Mathematics Subject Classification ID: 53C35
Mathematics Subject Classification ID: 53B25
zbMATH DE Number: 806238
zbMATH Keywords: principal orbits
zbMATH Keywords: isotropy subgroups
zbMATH Keywords: Riemannian symmetric spaces
zbMATH Keywords: isoparametric submanifolds
zbMATH Keywords: shape operator
reviewed by: Lieven Vanhecke
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01266321
OpenAlex ID: W13895668
description: scientific article; zbMATH DE number 806238